http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
SOME FUNCTIONAL IDENTITIES ARISING FROM DERIVATIONS
Abdellah Mamouni,Lahcen Oukhtite,Mohammed Zerra Korean Mathematical Society 2023 대한수학회논문집 Vol.38 No.1
This paper considers some functional identities related to derivations of a ring R and their action on the centre of R/P where P is a prime ideal of R. It generalizes some previous results that are in the same spirit. Finally, examples proving that our restrictions cannot be relaxed are given.
Commutativity criteria of prime rings involving two endomorphisms
Souad Dakir,Abdellah Mamouni,Mohammed Tamekkante 대한수학회 2022 대한수학회논문집 Vol.37 No.3
This paper treats the commutativity of prime rings with involution over which elements satisfy some specific identities involving endomorphisms. The obtained results cover some well-known results. We show, by given examples, that the imposed hypotheses are necessary.
COMMUTATIVITY WITH ALGEBRAIC IDENTITIES INVOLVING PRIME IDEALS
Mir, Hajar El,Mamouni, Abdellah,Oukhtite, Lahcen Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.3
The purpose of this paper is to study the structure of quotient rings R/P where R is an arbitrary ring and P is a prime ideal of R. Especially, we will establish a relationship between the structure of this class of rings and the behavior of derivations satisfying algebraic identities involving prime ideals. Furthermore, the characteristic of the quotient ring R/P has been determined in some situations.
ON JORDAN IDEALS IN PRIME RINGS WITH GENERALIZED DERIVATIONS
Bennis, Driss,Fahid, Brahim,Mamouni, Abdellah Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.3
Let R be a 2-torsion free prime ring and J be a nonzero Jordan ideal of R. Let F and G be two generalized derivations with associated derivations f and g, respectively. Our main result in this paper shows that if F(x)x - xG(x) = 0 for all $x{\in}J$, then R is commutative and F = G or G is a left multiplier and F = G + f. This result with its consequences generalize some recent results due to El-Soufi and Aboubakr in which they assumed that the Jordan ideal J is also a subring of R.
Hanane Aharssi,Kamal Charrabi,Abdellah Mamouni 대한수학회 2024 대한수학회논문집 Vol.39 No.1
This article examines the connection between 3-derivations and the commutativity of a prime ring $R$ with an involution $\ast$ that fulfills particular algebraic identities for symmetric and skew symmetric elements. In practice, certain well-known problems, such as the Herstein problem, have been studied in the setting of three derivations in involuted rings.
Generalized derivations in ring with involution involving symmetric and skew symmetric elements
Souad Dakir,Hajar El Mir,Abdellah Mamouni 대한수학회 2024 대한수학회논문집 Vol.39 No.1
In this paper we will demonstrate some results on a prime ring with involution by introducing two generalized derivations acting on symmetric and skew symmetric elements. This approach allows us to generalize some well known results. Furthermore, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.